In short, the technique of incremental training [1]} partitions the original DNN into each layers and trains the partitioned network by gradually increasing the number of layers. In our maximum hands-off control problem, the smaller \(p\)  tends to yield the sparser control input sequence.
However, we observed the use of small \(p\)  from the beginning does not yield an optimal solution.
Thus, we start with a large \(p\)  (e.g., \(p_0 = 1\) ) and decrease the value of \(p\)  gradually as the incremental training proceeds.
